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Analysis Details of SPIRE Photmeter Beam Profiles

( Bernhard Schulz, October 2014)

Initial Beam Profile

The beam profile was reconstructed from four fine scan maps with obsids: 1342186522, 1342186523, 1342186524, 1342186525, and two observations of the same sky region 1342255134 and 1342255135 three years later. The Neptune observations followed the small proper motion of the object. The scan pattern had, unlike standard scan map observations, very narrowly spaced scan legs. The maps scanning in spacecraft-y direction consisted of 150 scan legs separated by 3.9", the orthogonally scanning maps comprised of 210 scans at the same separation. There were actually two sets of each map, each starting in opposite directions to test for dependencies on scan direction. The second set of scans in Y-direction actually started mid-way between the previous +Y scan legs (2" offset), leading to an overall finer spacing of legs along the Z-coordinate. The +Z and -Z directions started with almost perfect overlap.Neptune moved about 6.1" between the mid-points of the first and last observation. The observations were special calibration observations that yielded a number of calibration results, for example the positions of all detector pixels, relative flatfields, and the ratio between integral and peak based flatfields, the so-called extended source gains.

Table 1: Observation IDs, times and positions of all six maps.

The last two "shadow" observations were made after Neptune had left the region 3 years later at about the same time of year to ensure the same observing geometry w.r.t the Zodiacal cloud. These were performed in a non-moving reference frame with the same narrow scan pattern as the Neptune observations. Each scan direction was executed only once. The duration of each map was equivalent to the corresponding ones on Neptune, i.e. spending a total of half the observing time that was used on Neptune.

The data processing started with standard archival data reduced with HIPE 12.1 and HIPE 11.1. The differences between these versions are irrelevant for products at Level 1. HIPE 13.0.3221 was used for destriping and map-making. We had to resort to an, at the time, very new development version of HIPE to have newly discovered issues with the initial median timeline subtraction of the destriper fixed. Another issue causing cross-like "shadows" was avoided by excluding the central 5' around Neptune from the destriping procedure.

The reduction steps were as follows:

Correct for SSO proper motion

Assemble all Level 1 timelines (4 observations for Neptune, 2 for Shadow) into one Level1 product.

Find all readouts within 5' radius from Neptune and set the Master flag as well as flag #5, unless the master flag was already set (only Neptune observations).

Run the Destriper.

For all readouts that had been deselected previously, indicated by bit #5, reset master bit and bit #5 (only Neptune observations).

Run Naive Mapper on destriped level 1 data twice, once with pixel size 1" and once with standard pixel size.

Background Subtraction

Although Neptune and shadow maps appear very consistent in its background features at first sight, a direct subtraction of the maps (see Fig. 3 left) shows a number of artifacts hinting at a small astrometric shift between both maps and a photometric difference. This is particularly obvious when using the maps at standard pixel size benefitting from higher S/N. The shadow map over-subtracts the sources by about 10%. Scaling down the shadow map by 10% gives a better removal, however the best background subtraction was achieved empirically by Gaussian smoothing of the shadow maps with sigmas = [0.10", 0.03", 0.10"] for PSW, PMW PLW respectively and shifting the PSW and PMW by 1.8" in the spacecraft X-direction. The smoothing of the shadow map effectively accounts for the smearing of the background galaxies in the Neptune images that were observed while the map center tracked the proper motion of the planet.

Figure 3: Difference maps of Neptune and shadow maps for PSW without any correction (left) and with a small shift by 1.8" in spacecraft X-direction and Gaussian smoothing of the shadow map with sigma=0.1" before the subtraction (right).

With the advent of the shadow maps, previous efforts involving detection and subtraction of point sources, and fitting of a warped background plane, became unnecessary. Removing the warped plane still gives the best agreement between the radial profiles of three arbitrary sectors chosen around the source, yet lacking a good motivation for either, removal of a warped plane or a flat tilted plane is missing now. The solid angles derived by integrating over the beam profile after removing optimized versions of a warped plane, a flat tilted plane, and a simple median are in Table 2.

PSW

PMW

PLW

Removed warped plane

448

800.4

1700.0

Removed flat tilted plane

447.1

801.8

1700.0

Removed median

447.2

800.9

1700.6

Table 2: Variations in integrated solid angle due to different background removal procedures.

The subtraction of the background observations has minimized the differences delivered by these various methods. Visual inspection of the background subtracted maps shows that for the 1" resolution maps the useful area stops outside of 750" because of too many NaNs. Thus we choose subtracting the simple median of all data points between 600" and 750" radius around the center.

Looking for "Triton Contamination"

Neptune's moon Triton could in principle affect the beam profile by adding flux to one side. Overplotting the positions of Triton during the observational time of all four maps over a contour plot of the reconstructed beam profile reveals no obvious deformation that could have been caused by its Submm emission. The FWHM of the beam is rather more narrow towards the moon's position.

Figure 4: Overplot of Triton positions during the observation over PSW isophotes of the Neptune map as thick black trace. The levels are in Jy and the small tick marks on the side are arc seconds.

Radial Beam Profiles

Since the ellipticity of the beam is moderate a radial beam profile can be calculated to study the far field at a better S/N. The beam center is fitted with a Gaussian, and average map values within concentric annuli of 1" radial difference around that center are calculated. Plots of these profiles versus radius are shofn in Figure 5.

Figure 5: TBW.

Editing done up to here

Solid Angles

After background tilt subtraction and background source removal the signal was averaged over concentric annuli around the source and this radialized beam profile was plotted against radius (Plot 1). To ensure symmetry, e.g. flatness of the background, the same was also plotted for three sectors (Plot 2 and 3). From the radialized beam profile a new background was determined and subtracted based on the necessity to have only positive flux within the errors (Plot 4).
The average background outside a given radius was plotted for all radii (Plot 5). The integrated solid angle within a given radius was plotted for all radii (Plot 6). All the aforementioned diagrams are seen for the three detector arrays in files:

This map shows green rings at 600, 650, and 1000 arcsec radius. The maps become less reliable outside of about 700 arcsec due to decreasing coverage and S/N. The background seems to rise again in the plots of average annular signal vs. radius, which is likely to be due to the lower coverage.

Results

The diagrams showing solid angle vs. radius show a plateau around 600 arcsec which may signal the end of significant contribution from the beam profile. At different integration radii, the following values in arcsec^2 result:

These data are between 3.6 and 6.7% different from the North&Griffin numbers for 1000 arcsec integration radius and between 2.0 and 3.9% for 600 arcsec integration radius.

SPIRE plans to conduct shadow observations of the same region on the sky without Neptune in it in the fall of 2012. These will be used to determine whether the apparent rise outside 700 arcsec is real and they will improve the accuracy of the background level determination substantially, especially for the longer wavelength observations.

A presentation of this data was given to the HCalSG, the Hfi/Spire Cross Calibration Group and the SDAG.

Errors

Another presentation was given at the SDAG, which discussed various sources of uncertainties and concluded that an error of +/- 4% is a conservative estimate at this time.

Correction between Isophotal and Reference Wavelength

It is important to point out that solid angles are color dependent. The FWHM of the beam varies with frequency proportional to nu^gamma. The most recent estimate from Griffin (priv. comm) for gamma is 0.78, 0.85, 0.85, respectively for PSW, PMW and PLW.

As the beam profiles and the solid angles were derived from a map of Neptune, there is a discrepancy to the n*Fnu = const. spectrum that all photometry is color corrected for.

To determine the magnitude of this variation, a radial beam profile model was derived from the final background subtracted 2D beam profiles, following the idea in Griffin et al. 2013. The radial beam profiles (download page) are split up into a constant and a variable core part whose radial scale varies with nu^gamma as mentioned above. The solid angle can be found by integrating the product of beam profile, relative spectral response function (RSRF) and source spectrum over radius and wavelength and dividing by the integral over RSRF and source spectrum. The source spectrum for Neptune was approximated by a power law with exponent -1.39. The ratio of the solid angles found for the Neptune power law and a power law with exponent -1 was used to correct the Neptune solid angles to the standard SPIRE reference spectrum.